the function graphed to the right is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x…

the function graphed to the right is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. determine the equation of the graph. y = □ (type an expression using x as the variable.)

the function graphed to the right is of the form y = c + cos x, y = c + sin x, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. determine the equation of the graph. y = □ (type an expression using x as the variable.)

Answer

Explanation:

Step1: Analyze the vertical - shift

The standard cosine function $y = \cos x$ has a range of $[- 1,1]$. The given graph has a range of $[1,3]$. The mid - value of the range of the given function is $\frac{1 + 3}{2}=2$. For $y=\cos x$, the mid - value is $0$. So, there is a vertical shift of $c = 2$.

Step2: Analyze the phase - shift

The standard cosine function $y=\cos x$ has a maximum at $x = 0$. The given cosine - like function has a maximum at $x = 0$. So, the phase - shift $d = 0$. The function is of the form $y=c+\cos x$. Substituting $c = 2$ and $d = 0$ into the form, we get $y=2+\cos x$.

Answer:

$y = 2+\cos x$